Question

D, E, F are the midpoints of the sides AB, BC, and CA of a triangle ABC, respectively.

i) If AB = 6.2cm, find DE.
ii) If DF = 3.8cm, find AC
iii) If the perimeter of triangle ABC is 21cm, find FE
a) DE = 3.1cm, AC = 12.4cm, FE = 5.5cm
b) DE = 1.9cm, AC = 7.6cm, FE = 3.5cm
c) DE = 2.3cm, AC = 9.2cm, FE = 4.1cm
d) DE = 4.2cm, AC = 16.8cm, FE = 7.3cm

Answer 1

Using properties of midsegments in a triangle, DE is calculated as half of AB yielding 3.1cm, AC is twice DF at 7.6cm, and FE is equal to DF, which is 3.8cm. The correct options are not listed in the student's provided multiple choices.

Step-by-step explanation:

To solve the student's problem regarding midpoints in a triangle, we need to use the properties of the midsegment in a triangle, which connects the midpoints of two sides of the triangle.

1. DE as a midsegment of triangle ABC is parallel to AB and half its length. Since AB = 6.2cm, DE = AB/2 = 6.2cm / 2 = 3.1cm.
2. AC as twice the length of DF (since DF is the midsegment), we have AC = 2 * DF = 2 * 3.8cm = 7.6cm.
3. Because DF and FE together span the entire length of AC, if AC is 7.6cm and DF is 3.8cm, then FE must be the remainder of that length, which is also 3.8cm.

Therefore, the correct answers are: a) DE = 3.1cm, b) AC = 7.6cm, c) FE = 3.8cm. The correct option is not listed in the provided choices, indicating a typo in the question options.